If f(x)= x - {x}^(2) find f(2+h) and f(x+h) where h is not equal to 0​

Question

If f(x)=

`x - {x}^(2)`
find f(2+h) and f(x+h) where h is not equal to 0​

Answer 1

f(2+h)=-(h+2/3)^2+1/4

f(x+h)=-(x+h-1/2)^2+1/4

Explanation:

1. f(2+h)=(2+h)-(2+h)^2=2+h-4-4h-h^2=-h^2-3h-2=-(h^2+3h+2)

=-(h+2/3)^2+1/4

2. Let (x+h)=a, then rewrite the equation into f(a)=a-a^2.

a-a^2=-(a^2-a)=-[(a-1/2)^2-1/4]=-(a-1/2)^2+1/4.

Insert a=x+h, f(x+h)=-(x+h-1/2)^2+1/4